Abstract
In this paper, a class of optimization problems with cone constraints in groups and semigroups is investigated by exploiting the image space analysis. Optimality is proved by means of separation arguments in the image space associated with the given problem, which turns out to be equivalent to the existence of saddle points of generalized Lagrangian functions under suitable assumptions. In particular, Lagrangian-type sufficient or necessary optimality conditions are obtained by introducing convex-like functions and using separation theorems between convex sets in groups and semigroups obtained by Li and Mastroeni.
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The authors would like to thank two anonymous referees and Professor Nguyen Dong Yen for their constructive criticism and helpful remarks which allowed us to improve the original presentation.
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Communicated by Nguyen Dong Yen.
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This work was supported by the National Natural Science Foundation of China (11871059, 11371015), the Applied Basic Project of Sichuan Province (2020YJ0111), the Innovation Team of Department of Education of Sichuan Province (16TD0019) and the Meritocracy Research Funds of China West Normal University (17YC379)
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Li, J., Mastroeni, G. Optimization Problems with Cone Constraints in Groups and Semigroups: An Approach Based on Image Space Analysis. J Optim Theory Appl 196, 973–1007 (2023). https://doi.org/10.1007/s10957-023-02161-z
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DOI: https://doi.org/10.1007/s10957-023-02161-z